The overtures to Peres reflect the Nobel laureate’s late-career star power and the dearth of viable challengers in Israel’s fragmented opposition to Prime Minister Benjamin Netanyahu.

Hopes for a Peres candidacy are ‘‘an act of desperation,’’ said political scientist Avraham Diskin. ‘‘It shows that there is a large vacuum in the center. They’re unable to join ranks, so they’re looking for miracles.’’

Netanyahu, riding high in the polls, recently tried to solidify his bid for reelection by joining forces with his foreign minister, Avigdor Lieberman.

Running on a joint list, Netanyahu’s Likud Party and Lieberman’s Yisrael Beitenu are expected to win more than 40 parliamentary seats. That reflects their separate strength in the polls, not more, but together they would form by far the largest faction in the 120-seat Parliament and put Netanyahu in a strong position for another term as prime minister.

The partnership has fueled calls for centrist parties to band together.

Polls show that a unified bloc of the Labor, Kadima, Yesh Atid, and Independence parties could rival Netanyahu’s hard-line bloc. A poll in the Yediot Ahronot daily Friday found that a center-left bloc plus parties representing Israel’s Arabs could win 59 seats, almost enough to block Netanyahu.

Although the centrist parties share similar ideologies, particularly a softer line toward peacemaking with the Palestinians, their leaders have shown little interest in unifying. Peres could be one of the few figures capable of rallying these parties behind him. He also may be best positioned to do so.

Ehud Olmert, a former prime minister and another potential heavyweight candidate, is in the midst of a bribery trial and has not decided whether to seek office again.

Peres brings to the table a résumé that is unmatched.

After more than six decades in politics, he is the ultimate political survivor with the gravitas to take on Netanyahu. Winner of the 1994 Nobel Peace Prize, he mingles among the world’s rich and famous, receiving rock star welcomes at conferences and ceremonies around the globe. He has a good relationship with both the Palestinians and the White House.

As president, he has cultivated an image as a sage, grandfatherly figure, calming the nation in his deep, monotone voice during times of trouble. He has also courted younger Israelis, embracing social media and backing high-tech industries.

An official in Peres’s office said that over the last few weeks, a number of operatives with ties to centrist parties, as well as retired military officials, approached him about leading a unified bloc. The official declined to identify the people who had spoken to Peres and spoke on condition of anonymity.

While describing the pressure as ‘‘heavy,’’ the official said Peres had no intention of leaving the presidency, saying he was committed to finishing the remaining two years of his term.

Messages to Labor and Kadima were not returned, while officials with Yesh Atid and Independence said they were not trying to enlist Peres.

If Peres returns to party politics, that image he has built as president could crumble.

For years, Peres had a reputation as a nasty but losing political operator, due to his inability to win an election. Of his three previous stints as prime minister, two were in a caretaker capacity and a third was in a power-sharing arrangement after elections ended in stalemate.

Only late in life, at 83, was he elected president in a parliamentary vote.